The 2009/10 Premier League champions announced late on Monday that they had made a proposal to buy back the freehold land at Stamford Bridge from Chelsea Pitch Owners (CPO).
Chelsea said this did not mean the club would definitely be relocating but added that buying back the freehold removed a potential hurdle "should a suitable [alternative] site become available in the future".
"I have heard rumours for quite some time they are looking to move but it remains to be seen what will actually happen," Harris told Reuters in an interview on Tuesday.
"It seems as though they can't extend Stamford Bridge's capacity so moving is probably the only thing they can do. If it's good for the club I'd go along with it."
CPO was a company set up in 1993, at a time when the ground was under threat from property developers, to ensure the ownership of the site was placed in club-friendly hands.
Now that Chelsea are owned by billionaire Russian Roman Abramovich, the Londoners believe that safeguard is no longer necessary.
"Chelsea should always be grateful to those who invested in CPO," chairman Bruce Buck said in a statement. "We know only too well how close the club came to losing our home prior to the formation of CPO.
"But that threat has now gone under Mr Abramovich's ownership and with the CPO structure in place we cannot plan with certainty for the future. I hope all CPO shareholders vote in favour of the proposal."
FINANCIAL SENSE
Harris, who played a record 795 games for the club and was skipper when they won the 1970 FA Cup and 1971 European Cup Winners' Cup, said a move away from Stamford Bridge would make financial sense.
"The capacity is 41,000 right now so I suppose if they can get a bigger stadium that takes 60,000 it brings in more money," said the 66-year-old former hard-man defender.
"You'll obviously have some people for it and some people against it but... if it makes Chelsea a bigger club then I can't see anything wrong with it."
Chief Executive Ron Gourlay underlined the fact that a move was by no means certain.
"Chelsea Football Club and Mr Abramovich are determined to ensure the club continues to compete at the highest level of world football," said Gourlay.
"We continue to look at options for expanding the Bridge and I should be clear we have not identified a site for a new stadium elsewhere."
Harris, who does corporate hospitality work at Stamford Bridge, has a suite named after him at the ground.
"The biggest suite at Chelsea is the Ron Harris suite which I'm proud of," he explained. "That was never done under the previous regime so I've got great admiration for everything Roman Abramovich has done for the club and for me personally.
"Maybe they would build me a new Ron Harris suite if they moved to a new ground."
